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98                         ANALYTICAL MECHANICS
acceleration.   Therefore the unit is the ^~?2.   The dimen-
oC'C'*
sions of angular acceleration are given by [T~2].
ILLUSTRATIVE EXAMPLE. A particle moves so that the coordinates of its position at any instant
are given by the equations
x — a cos kt, y = a sin kt.
Find the acceleration and its components.
In a previous illustrative example, p. 82,  it was shown that these
equations represent uniform circular motion, with the following data:
v = ka,                                       co = kj
vx = — ka sin kt,                         vr = 0,
vy — ka cos kt,                           vp = ka.
Therefore
,
— — K X)                              dt
= — k~ a sin kt       f _ 1 d
/  = - Fa,             w =   -k = 0,                       = - to2.
W6
It will be observed that fr has a value different from zero, while vr is nil.
PROBLEMS.
1.  A flywheel making 250 revolutions per minute is brought to rest in 2 minutes.   Find the average angular acceleration.
2.   A flywheel making 250 revolutions per minute is retarded by a
constant acceleration of — 5 -^~- .   How many revolutions will the flv-
sec.2                                                     J
wheel make before stopping?
3.   In the preceding problem find the time it takes the flywheel to 3ome to rest.
4.  Find the angular velocity and angular acceleration of a particle moves in a manner defined by the following pairs of equations :
(a)  p = a sin cotf,   6 — b sin cat.
(b)  p = a sin cot,   6 = 1} cos coZ.
(c)  p = a sin co£,   6 = bt.
(d)  p = ae**,        o = bt.
5.   In problem 4 find the equation of the path and plot it.